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- Title
Grassmannian kriging with applications in POD-based model order reduction.
- Authors
Mosquera, Rolando; Falaize, Antoine; Hamdouni, Aziz
- Abstract
In this work, we propose a generalization of the kriging interpolation procedure from Euclidean spaces to Grassmann manifolds in the context of model order reduction based on Proper Orthogonal Decomposition (POD). This generalization relies on the introduction of a so-called geodesic experimental semi-variogram which depends solely on the repartition of the interpolation values on the manifold. Here, the interpolation values are the subspaces engendered by the bases obtained by POD of the solutions associated with sampling parameters. Three CFD applications are presented: (i) the two-dimensional flow pas a cylinder in a channel, (ii) the two-dimensional Burger equation and (iii) the one dimensional wave equation. For each application, the proposed method to compute the interpolated basis associated with a given parameter proves faster than state-of-the-art method while achieving the same accuracy.
- Subjects
PROPER orthogonal decomposition; KRIGING; GRASSMANN manifolds; WAVE equation; BURGERS' equation
- Publication
Discrete & Continuous Dynamical Systems - Series S, 2024, Vol 17, Issue 7, p1
- ISSN
1937-1632
- Publication type
Article
- DOI
10.3934/dcdss.2024017